A de Finetti representation theorem for infinite dimensional quantum systems and applications to quantum cryptography

According to the quantum de Finetti theorem, if the state of an N-partite system is invariant under permutations of the subsystems then it can be approximated by a state where almost all subsystems are identical copies of each other, provided N is sufficiently large compared to the dimension of the subsystems. The de Finetti theorem has various applications in physics and information theory, where it is for instance used to prove the security of quantum cryptographic schemes. Here, we extend de Finetti's theorem, showing that the approximation also holds for infinite dimensional systems, as long as the state satisfies certain experimentally verifiable conditions. This is relevant for applications such as quantum key distribution (QKD), where it is often hard - or even impossible - to bound the dimension of the information carriers (which may be corrupted by an adversary). In particular, our result can be applied to prove the security of QKD based on weak coherent states or Gaussian states against general attacks.Comment: 11 pages, LaTe

Itinerant in-plane magnetic fluctuations and many-body correlations in Nax_xCoO2_2

Based on the {\it ab-initio} band structure for Na$_x$CoO$_2$ we derive the single-electron energies and the effective tight-binding description for the $t_{2g}$ bands using projection procedure. Due to the presence of the next-nearest-neighbor hoppings a local minimum in the electronic dispersion close to the $\Gamma$ point of the first Brillouin zone forms. Correspondingly, in addition to a large Fermi surface an electron pocket close to the $\Gamma$ point emerges at high doping concentrations. The latter yields the new scattering channel resulting in a peak structure of the itinerant magnetic susceptibility at small momenta. This indicates dominant itinerant in-plane ferromagnetic fluctuations above certain critical concentration $x_m$, in agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a tendency towards the antiferromagnetic fluctuations. We further analyze the many-body effects on the electronic and magnetic excitations using various approximations applicable for different $U/t$ ratio.Comment: 10 page

Relation between Vortex core charge and Vortex Bound States

Spatially inhomogeneous electron distribution around a single vortex is discussed on the basis of the Bogoliubov-de Gennes theory. The spatial structure and temperature dependence of the electron density around the vortex are presented. A relation between the vortex core charge and the vortex bound states (or the Caroli-de Gennes-Matricon states) is pointed out. Using the scanning tunneling microscope, information on the vortex core charge can be extracted through this relation.Comment: 5 pages, 3 figures; minor changes; Version to appear in JPSJ 67, No.10, 199

Determination of the Coherence Length and the Cooper-Pair Size in Unconventional Superconductors by Tunnelling Spectroscopy

The main purpose of the paper is to discuss a possibility of the determination of the values of the coherence length and the Cooper-pair size in unconventional superconductors by using tunnelling spectroscopy. In the mixed state of type-II superconductors, an applied magnetic field penetrates the superconductor in the form of vortices which form a regular lattice. In unconventional superconductors, the inner structure of a vortex core has a complex structure which is determined by the order parameter of the superconducting state and by the pairing wavefunction of the Cooper pairs. In clean superconductors, the spatial variations of the order parameter and the pairing wavefunction occur over the distances of the order of the coherence length and the Cooper-pair size, respectively. Therefore, by performing tunnelling spectroscopy along a line passing through a vortex core, one is able, in principle, to estimate the values of the coherent length and the Cooper-pair size.Comment: 13 pages, including 17 figure

The Structure of a Vortex in the t-J Model

We study the single-vortex solution of the t-J model within resonating-valence-bond (RVB) mean-field theory. We find two types of vortex cores, insulating and metallic, depending on the parameters of the model. The pairing order parameter near both cores have $d_{x^2 -y^2}+i\eta d_{xy}$ symmetry. For some range of $t/J$ the calculated tunneling spectrum of the metallic vortex core agrees qualitatively with the STM tunneling data for BSCCO

Theory of vortex lattice effects on STM spectra in d-wave superconductors

Theory of scanning tunneling spectroscopy of low energy quasiparticle (QP) states in vortex lattices of d-wave superconductors is developed taking account of the effects caused by an extremely large extension of QP wavefunctions in the nodal directions and the band structure in the QP spectrum. The oscillatory structures in STM spectra, which correspond to van Hove singularities are analysed. Theoretical calculations carried out for finite temperatures and scattering rates are compared with recent experimental data for high temperature cuprates.Comment: 4 pages, 3 eps figures, M2S-HTSC-VI conference paper, using Elsevier style espcrc2.st

Kohn-Luttinger instability of the t-t' Hubbard model in two dimensions: variational approach

An effective Hamiltonian for the Kohn-Luttinger superconductor is constructed and solved in the BCS approximation. The method is applied to the t-t' Hubbard model in two dimensions with the following results: (i) The superconducting phase diagram at half filling is shown to provide a weak-coupling analog of the recently proposed spin liquid state in the J_1-J_2 Heisenberg model. (ii) In the parameter region relevant for the cuprates we have found a nontrivial energy dependence of the gap function in the dominant d-wave pairing sector. The hot spot effect in the angular dependence of the superconducting gap is shown to be quite weak

Strong diamagnetic response and specific heat anomaly above T_c in underdoped La_(2-x)Sr_xCuO_4

By measuring AC susceptibility using a very low amplitude of the AC field (<1 mG) it is shown that underdoped samples of La_(2-x)Sr_xCuO_4 (LASCO), are diamagnetic in a temperature region above T_c up to a temperature T^*. This behavior is only observed with AC fields along the c-axis whereas for fields in the ab-plane no diamagnetism above Tc was detected. The diamagnetism is almost frequency independent in the frequency range 0.1-10 kHz. At T* a broad step anomaly in the specific heat is inferred through measurements of the elastic constant c33. We suggest that the observed diamagnetism and the anomaly in the elastic constant are associated with the existence of phase incoherent Cooper pairs between Tc and T*.Comment: 5 pages 7 figures, to appear in Phys. rev

Instability of a Landau Fermi liquid as the Mott insulator is approached

We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the 4 points $(\pm \pi/2, \pm \pi/2)$ as the electron density is increased. Umklapp processes at the 4 patches near $(\pm \pi/2, \pm\pi/2)$ lead the renormalization group equations to scale to strong coupling resembling the behavior of a 2-leg ladder at half-filling. The incompressible character of the fixed point causes a breakdown of Landau theory at these patches. A further increase in density spreads the incompressible regions so that the open Fermi surface shrinks to 4 disconnected segments. This non-Landau state, in which parts of the Fermi surface are truncated to form an insulating spin liquid, has many features in common with phenomenological models recently proposed for the cuprate superconductors.Comment: Minor changes. LaTeX2e, 12 pages, 5 figures. J. Phys. CM 10 (1998) L38

Truncation of a 2-dimensional Fermi surface due to quasiparticle gap formation at the saddle points

We study a two-dimensional Fermi liquid with a Fermi surface containing the saddle points $(\pi,0)$ and $(0,\pi)$. Including Cooper and Peierls channel contributions leads to a one-loop renormalization group flow to strong coupling for short range repulsive interactions. In a certain parameter range the characteristics of the fixed point, opening of a spin and charge gap and dominant pairing correlations are similar to those of a 2-leg ladder at half-filling. An increase of the electron density we argue leads to a truncation of the Fermi surface with only 4 disconnected arcs remaining.Comment: Reference added. RevTeX 4 pages incl. 4 ps file